Recent content by phosgene

Thanks for that, I'll go back to the drawing board and see what I can come up with.

Hi, thanks for the reply. The book doesn't cover the technique you mention and I don't know how to do it. The question references a previous one in which the particles aren't accelerating and the method is to use a Lorentz transform for velocity.

Homework Statement A particle P undergoes the hyperbolic motion x_{P}(t) = \frac{c}{a}(c^2 + a^2 t^2)^\frac{1}{2} along the x-axis of frame S, where c is the speed of light and a is a constant. A second particle, Q, undergoes the motion x_{Q}(t) = \frac{1}{2}ct + \frac{c^2}{a} and so...

Ok, I went back and plugged the numbers into the relation andrewkirk pointed me to: RMSE=\sqrt{1-r^2}SD_{y} The value for the RMSE is ~16.5, whereas the value for SD of the data is ~16.7. The correlation coefficient r is given as 0.6516. With these numbers, the right side of the equation...

Ah, I think I got it now. Thanks!

Thanks for the reply. Does this mean the standard deviation of my data points isn't related to the RMSE of the regression line? The question is specifically referring to that SD. And it's very similar to the value for the RMSE of the regression line. As far as I can tell, this will say nothing...

Homework Statement I'm being asked to compare the standard deviation of a data set with the root mean square error of the regression line used to model the data, in order to determine the reliability of the regression line. Homework Equations Mean squared error = variance + bias squared The...

Homework Statement Maximise the volume of a rectangular prism with the following constraints: the surface area must equal 2m^2 and the total edge length must be 12m. Homework Equations Using Lagrange multipliers, we construct the function we want to optimise with h(x,y,z, λ_{1}...

Thanks for the reply, but I have the solution now. The key step was (for anyone else who might be having trouble with a question similar to this) to recognize that |∑_{j} c_{ij}x_{j} - c_{ij}y_{j}| ≤ ∑_{j} |c_{ij}x_{j} - c_{ij}y_{j}| and then to note how |x_{j} - y_{j}| ≤...

Homework Statement Consider the metric space (R^{n}, d_{∞}), where if \underline{x}=(x_{1}, x_{2}, x_{3},...,x_{n}) and \underline{y}=(y_{1}, y_{2}, y_{3},...,y_{n}) we define d_{∞}(\underline{x},\underline{y}) = max_{i=1,2,3...,n} |x_{i} - y_{i}| Assume that (R^{n}, d_{∞}) is...

Thanks for the replies everyone. I was leaning toward complex analysis and judging from the replies here, it wouldn't be a bad choice. So complex analysis it is!

Hi guys. It's almost time to choose my courses for this year. I'm torn between taking PDE's due to how important it is for physics, or complex analysis due to just liking pure maths. If I do well enough, I'm *possibly* looking to do further study in mathematical physics. I was thinking that if...

Homework Statement In the diagram below, masses m and Me are in circular orbit about Ms with the same period. http://min.us/i/lprtU83D9cGR Derive an expression for the equilibrium position r of mass m. Homework Equations For a circular orbit, the eccentricity, e = 0...

Homework Statement Let f_{n}(x)=\frac{x}{1+x^n} for x \in [0,∞) and n \in N. Find the pointwise limit f of this sequence on the given interval and show that (f_{n}) does not uniformly converge to f on the given interval. Homework Equations The Attempt at a Solution I found that the pointwise...

I misread it, thought that the corollary was about dependence too. :redface: